Space of modular forms of level 88 and weight 6

• Label: 88.6
• Level: 88
• Weight: 6
• Dimension: 645
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 2880
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2880\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(88))\).

	Total	New	Old
Modular forms	1260	681	579
Cusp forms	1140	645	495
Eisenstein series	120	36	84

Trace form

645 * q - 6 * q^2 - 50 * q^3 - 50 * q^4 + 148 * q^5 + 222 * q^6 - 154 * q^7 + 486 * q^8 - 6 * q^9 - 1274 * q^10 - 134 * q^11 - 3172 * q^12 - 956 * q^13 + 4758 * q^14 + 4772 * q^15 + 6614 * q^16 + 4686 * q^17 - 9518 * q^18 - 8333 * q^19 - 9258 * q^20 - 7860 * q^21 + 5626 * q^22 - 7750 * q^23 + 15574 * q^24 - 1454 * q^25 - 11226 * q^26 + 16795 * q^27 - 10314 * q^28 + 12874 * q^29 + 6676 * q^30 + 20692 * q^31 + 29664 * q^32 + 17687 * q^33 - 12276 * q^34 - 45532 * q^35 - 107282 * q^36 - 20652 * q^37 - 71020 * q^38 - 95038 * q^39 + 9996 * q^40 + 63038 * q^41 + 232568 * q^42 + 73846 * q^43 + 155452 * q^44 + 68266 * q^45 + 8440 * q^46 + 68372 * q^47 - 145052 * q^48 - 35064 * q^49 - 76444 * q^50 - 192935 * q^51 - 95440 * q^52 - 36352 * q^53 - 210186 * q^54 - 6776 * q^55 + 50644 * q^56 + 148479 * q^57 + 140812 * q^58 + 22063 * q^59 + 26056 * q^60 + 15984 * q^61 - 69002 * q^62 + 187676 * q^63 + 83830 * q^64 - 59236 * q^65 - 43234 * q^66 - 116996 * q^67 - 20698 * q^68 - 75560 * q^69 - 30224 * q^70 + 24754 * q^71 - 193916 * q^72 + 46250 * q^73 + 139112 * q^74 - 336545 * q^75 + 373782 * q^76 + 51806 * q^77 + 1105188 * q^78 - 40586 * q^79 + 396520 * q^80 - 152161 * q^81 - 442174 * q^82 + 25417 * q^83 - 977634 * q^84 + 195956 * q^85 - 533810 * q^86 + 423796 * q^87 - 1029754 * q^88 + 231306 * q^89 - 1204410 * q^90 + 275164 * q^91 - 77018 * q^92 + 140350 * q^93 + 507278 * q^94 + 626470 * q^95 + 988816 * q^96 + 18075 * q^97 + 1480264 * q^98 - 747628 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(88))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
88.6.a	\(\chi_{88}(1, \cdot)\)	88.6.a.a	2	1
		88.6.a.b	3
		88.6.a.c	4
		88.6.a.d	4
88.6.c	\(\chi_{88}(45, \cdot)\)	88.6.c.a	50	1
88.6.e	\(\chi_{88}(87, \cdot)\)	None	0	1
88.6.g	\(\chi_{88}(43, \cdot)\)	88.6.g.a	2	1
		88.6.g.b	56
88.6.i	\(\chi_{88}(9, \cdot)\)	88.6.i.a	28	4
		88.6.i.b	32
88.6.k	\(\chi_{88}(19, \cdot)\)	88.6.k.a	8	4
		88.6.k.b	224
88.6.m	\(\chi_{88}(7, \cdot)\)	None	0	4
88.6.o	\(\chi_{88}(5, \cdot)\)	88.6.o.a	232	4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(88))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(88)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 1}\)